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\author{五六七 }
\title{Hald水泥主成分回归 }

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\begin{document}

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\begin{abstract}
水泥释放的热量与其中的化学成分之间的回归模型。
\end{abstract}

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\section{问题描述}
使用水泥时会散发热量。其热量与含有的化学成分的额比例有一定关系。变量记号如表所示。

\begin{table}[ht!]\centering
\caption{变量名称与含义} \vspace{0.2cm}
\begin{tabular}{|p{2cm}|p{6cm}|p{2cm}|}\hline
变量名 & 含义 & 单位  \\ \hline 
$x_1$ & $3CaO\cdot Al_2O_3$ 的含量 & \% \\ \hline 
$x_2$ & $3CaO\cdot SiO_2$ 的含量 & \% \\ \hline 
$x_3$ & $4CaO\cdot Al_2O_3\cdot Fe_2O_3$ 的含量 & \% \\ \hline 
$x_4$ & $2CaO\cdot SiO_2$ 的含量 & \% \\ \hline 
$y$ & 热量 & cal \\ \hline  
\end{tabular}
\end{table}

Hald在其专著 \cite{hald1952} 中，给出了一些水泥的样本数据如下表所示。
\begin{table}[ht!]\centering
\caption{一些水泥样本的数据} \vspace{0.2cm}
\begin{tabular}{|M{1cm}|M{1cm}|M{1cm}|M{1cm}|M{1cm}|M{1cm}|}\hline 
序号 & $x_1$ & $x_2$ & $x_3$ & $x_4$ & $y$ \\ \hline 
1&	7	&26	&6	&60	&78.5 \\ \hline 
2&	1	&29	&15	&52	&74.3 \\ \hline 
3&	11	&56	&8	&20	&104.3 \\ \hline 
4&	11	&31	&8	&47	&87.6 \\ \hline 
5&	7	&52	&6	&33	&95.9 \\ \hline 
6&	11	&55	&9	&22	&109.2 \\ \hline 
7&	3	&71	&17	&6	&102.7 \\ \hline 
8&	1	&31	&22	&44	&72.5 \\ \hline 
9&	2	&54	&18	&22	&93.1 \\ \hline 
10&	21	&47	&4	&26	&115.9 \\ \hline 
11&	1	&40	&23	&34	&83.8 \\ \hline 
12&	11	&66	&9	&12	&113.3 \\ \hline 
13&	10	&68	&8	&12	&109.4 \\ \hline 
\end{tabular}
\end{table}

试构建热量关于化学成分不同含量的主成分回归模型。

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\section{建立模型}




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\section{编程计算}




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\section{检验模型}




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\section{回答问题}




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%\section{参考文献 }
\begin{thebibliography}{99}

%\bibitem{dingtongren} 丁同仁、李承治，常微分方程教程，高等教育出版社，2022年3月第三版。
\bibitem{sishoukui-2} 司守奎,孙玺菁. \emph{Python数学建模算法与应用}, 国防工业出版社. 2022年1月第1版. 
\bibitem{hexiaoqun-ara} 何晓群. \emph{应用回归分析(R语言版)}. 电子工业出版社. 2017年7月第1版. 
%\bibitem{dalgaard} Peter Dalgaard 著, 郝智恒等译. \emph{R语言统计入门}. 人民邮电出版社. 2014年6月第1版. 

\bibitem{woods1932} Woods, H., Steinour, H.H. and Starke, H.R. \emph{Effect of Composition of Portland Cement on Heat Evolved During Hardening}. Industrial Engineering and Chemistry 24: 1207–1214. 1932. 

\bibitem{hald1952} Hald, A. \emph{Statistical Theory with Engineering Applications}.(page 647.) New York; Wiley. 1952. 

\bibitem{Liu-biasing} R package liureg, \url{https://rdrr.io/cran/liureg/man/Hald.html}

\end{thebibliography}

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